Schumer, a New York Democrat, says he'd like to see an assault weapons ban pass, too. But he says passing gun control measures is not easy.

Because enforcing background checks on all gun purchases doesn't change the rules on who can own guns, Schumer says he sees it as "a way to come to the middle and get something real done." Right now, advocates say some 40 percent of gun sales occur without background checks, such as those at gun shows.

Schumer spoke to reporters at the Capitol Monday. Vice President Joe Biden is expected to endorse universal background checks in recommendations Tuesday to President Barack Obama.